1. Field of the Invention
The present invention relates generally to optical fiber signal transmission, and more particularly, to the generation of polarization-mode dispersion (PMD) to emulate the natural occurrence of PMD in optical fiber and to use PMD generation to compensate for PMD generated by optical fiber.
Optical fibers do not have perfect properties. Slight irregularities and asymmetries introduced during the manufacturing process, or during installation, lead to optical fibers with birefringence, a property whereby one particular optical polarization propagates slightly faster than the other. Furthermore, these perturbations vary randomly with distance and over time. The varying fiber properties produce random polarization state changes in a propagating optical signal, which when combined with the birefringence lead to signal distortion known as polarization mode dispersion (PMD).
Light propagating in an optical fiber possesses two optical polarizations, directions perpendicular to the axis of the fiber and to each other along which the oscillations of the electromagnetic field are aligned. In the case of birefringent materials, these two polarizations organize themselves into two principal polarization states that travel at different speeds. When an optical pulse is launched with an arbitrary input polarization, it is projected into the two principal states which then split or separate during propagation, resulting in temporal spreading known as differential group delay (DGD).
In optical fibers, birefringence arises either from manufacturing irregularities or from stresses introduced during cabling or installation, and varies randomly with distance and with time. In this case, the process of an optical pulse being decomposed into principal polarization states and splitting occurs randomly and continuously, leading to an increasing spreading of the pulse known as polarization mode dispersion (PMD). The average root-mean-square rate of spreading is known as the PMD coefficient, and is measured in units of ps/√{square root over (km)} for typical communications fibers [1,2].
An important measure of PMD is provided by the polarization dispersion vector, also called the PMD vector [2]. The magnitude of this vector is the differential group delay (DGD; also called first-order PMD), and its direction gives the principal polarization states. Because birefringence in a real fiber is random, in general the DGD is a random variable with a Maxwellian probability density function (pdf). Another important measure is the frequency derivative of the polarization dispersion vector, and is known as second-order PMD; this vector measures both polarization dependent chromatic dispersion and signal depolarization. While the first-order PMD or DGD describes the amount of the simplest form of pulse splitting caused by birefringence, second-order (and higher-order) PMD measures the amount of more complicated PMD-induced pulse distortions. In general, both the polarization dispersion vector and its frequency derivative are an important predictor of power penalties and outage probabilities caused by PMD.
With the increasing demand for larger optical transmission data rates, PMD has emerged as one of the major impairments to upgrading current per channel data rates to 10 Gbit/s and beyond in terrestrial wavelength-division-multiplexed (WDM) systems. For example, it has been reported that PMD is expected to be a significant problem at 40 Gbit/s, even in newly installed fiber. A key difficulty with PMD is that it is intrinsically a random phenomenon, and, as a consequence, the penalties it produces change not only randomly over distance because the fiber properties vary with distance, but also over time because the ambient temperature and other environmental parameters vary. In system design, a maximum power penalty is usually assigned to PMD, and one demands that the outage probability—that is, the probability of the PMD-induced penalty exceeding this allowed value—is very small, typically 10−6 or less. Because the desired outage probability is very small, it has been virtually impossible to use either Monte-Carlo simulations or laboratory experiments to determine it, due to the extremely large number of system configurations that must necessarily be explored in order to obtain a reliable estimate.
In the absence of effective tools for calculating outage probabilities, system designers have resorted to stopgap techniques. First of all, because desired outage probabilities are small, it is the tails of the probability distribution where large DGD values occur that are particularly important, since these rare events are the ones most likely to result in system outages. Because the direct calculation of probabilities in the tails of the pdf has not been feasible, an indirect technique that has been used is to produce artificially large DGD values, determine the penalties at these large DGDs, and then weight the results using the Maxwellian distribution. A fundamental problem with this method, however, is that there is no direct relationship between the DGD and the power penalty. In addition, different configurations of an optical fiber (or any other device with PMD) can give the same DGD but not contribute equally to the power penalty, and the relative weighting or importance of these configurations must be treated properly.
This problem is particularly acute when studying devices designed to be placed at the end of an optical fiber line to compensate the PMD accumulated during transmission. A stopgap approach for analyzing such systems consists of calculating the average DGD after PMD compensation, and then, assuming that the compensated DGD still obeys a Maxwellian distribution, to calculate the distribution of the power penalties and thus determine an estimate for the reduction in the outage probability. This approach is also seriously flawed, however, since recent work has made it clear that the DGD distribution in compensated systems is typically far from Maxwellian.
What is needed, of course, is a direct method that can determine the true probability of large PMD events. Such a method would allow PMD-induced penalties and the resulting outage probabilities to be correctly assessed.
A standard way of determining the effects of PMD is by using Monte-Carlo simulations, where random number generators are used to drive computational models of the physical variations described above. Similar techniques can be used experimentally; in this case, devices known as PMD emulators are used to generate the random PMD variations [3]. Because system designers require optical transmission systems to be extremely reliable, however, significant events (i.e., ones sufficiently serious to produce transmission errors) must by necessity be very rare. This requirement means that in a straightforward application of Monte-Carlo methods or experimental techniques, a prohibitively large number of results is needed to obtain accurate system statistics.